Solve for $x$ and $y$ using substitution. ${-6x-3y = 9}$ ${y = -6x+1}$
Since $y$ has already been solved for, substitute $-6x+1$ for $y$ in the first equation. ${-6x - 3}{(-6x+1)}{= 9}$ Simplify and solve for $x$ $-6x+18x - 3 = 9$ $12x-3 = 9$ $12x-3{+3} = 9{+3}$ $12x = 12$ $\dfrac{12x}{{12}} = \dfrac{12}{{12}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = -6x+1}\thinspace$ to find $y$ ${y = -6}{(1)}{ + 1}$ $y = -6 + 1$ $y = -5$ You can also plug ${x = 1}$ into $\thinspace {-6x-3y = 9}\thinspace$ and get the same answer for $y$ : ${-6}{(1)}{ - 3y = 9}$ ${y = -5}$